In this dissertation, we consider a class of two-team adversarial differential games in which there are multiple mobile dynamic agents on each team. We describe such games in terms of semi-infinite minmax Model Predictive Control (MPC) problems, and present a numerical optimization technique for efficiently solving them. We also describe the implementation of the solution method in both indoor and outdoor robotic testbeds.
Our solution method requires one to solve a sequence of Quadratic Programs (QPs), which together efficiently solve the original semi-infinite min- max MPC problem. The solution method separates the problem into two subproblems called the inner and outer subproblems, respectively. The inner subproblem is based on a constrained nonlinear numerical optimization technique called the Phase I-Phase II method, and we develop a customized version of this method. The outer subproblem is about judiciously initializing the inner subproblems to achieve overall convergence; our method guarantees exponential convergence.
We focus on a specific semi-infinite minmax MPC problem called the harbor defense problem. First, we present foundational work on this problem in a formulation containing a single defender and single intruder. We next extend the basic formulation to various advanced scenarios that include cases in which there are multiple defenders and intruders, and also ones that include varying assumptions about intruder strategies.
Another main contribution is that we implemented our solution method for the harbor defense problem on both real-time indoor and outdoor testbeds, and demonstrated its computational effectiveness. The indoor testbed is a custom-built robotic testbed named HoTDeC (Hovercraft Testbed for Decentralized Control). The outdoor testbed involved full-sized US Naval Academy patrol ships, and the experiment was conducted in Chesapeake Bay in collaboration with the US Naval Academy. The scenario used involved one ship (the intruder) being commanded by a human pilot, and the defender ship being controlled automatically by our semi-infinite minmax MPC algorithm.The results of several experiments are presented.
Finally, we present an efficient algorithm for solving a class of matrix games, and show how this approach can be directly used to effectively solve our original continuous space semi-infinite minmax problem using an adaptive approximation.